Café Tacuba played in front of 170,000 people earlier this month in downtown Mexico City, perhaps the biggest hometown send-off to precede a monthlong American tour in music history. This unfathomably expansive mass of humanity sang along loudly, producing sound waves that must have caused window-rattling tremors in adjacent towns. During the ballads, fans raised their cell phones in lieu of lighters, producing a luminous spectrum of glowing blue, yellow, and green.

"It was an emotional moment," bassist Quique Rangel says in a phone interview from Mexico City. "The heart of the city showed us love."

A gig at Cleveland's 1,200-capacity House of Blues might appear anticlimactic for a band with superstar-caliber credentials, including gold records and Grammys to its credit, but Rangel says his band looks forward to discovering the extent of its U.S. following.

"What we have seen through the shows in the United States is that even if we don't know about it, there's a Latin crowd in every city," he says. "Mexican people are looking for something with their roots, and even if they don't know the band well, they go and try to have a celebration. They use it as a tool to have a party, to relax and decompress all the stress."

When Café Tacuba released its definitive records, 1994's Re and 2003's Cuatro Caminos, awestruck American critics scanned their memories for similarly eclectic acts. Some might have considered Mr. Bungle's California, an inspired amalgam of doo-wop, garage-rock, polka, and psychedelic sounds, but recommending an eclectic, Spanish-singing act using a relatively obscure touchstone is a tough sell. So writers turned to likening Re to the Beatles' White Album and Cuatro Caminos to Radiohead's Kid A. (Cuatro's cover sticker bears this comparison, as printed in Alternative Press.)

It was a generous gesture, converting Café Tacuba's musical currency by using rock's gold standards, but it shortchanged the group. Tacuba might share an ambitious, adventurous nature with Radiohead, but it's essentially a good-times band whose joyous outbursts couldn't fall further from Kid A's chilly corporeal compositions. The Beatles had pure pop at their core, while Tacuba starts with traditional norteno, bolero, and mariachi melodies.

When the band formed in 1989, uniting four graphic-design students from Metropolitan Autonomous University, Café Tacuba emulated its American and British idols. Soon, though, its members realized that by aping the Pixies and the Smiths, they were muting their Mexican muse.

"We didn't have the sensibility to play as people from another culture," Rangel says. "We decided we must be who we are."

Initially, the group created a stir within the Mexican music community. Purists bristled at what they interpreted as ironic interpretations of sacred song structures.

"There was some controversy, but music evolves that way," Rangel says. "We treat the roots music in the most serious possible way, but we play with the elements. If it produces something different, we don't question that."

Very little changes when Café Tacuba plays American shows. It doesn't shorten its marathon three-hour sets unless a venue's curfew forces its hand. It doesn't sing in English, though charismatic frontman Rubén Albarrán does translate his frequent banter. The jovial Albarrán has changed his liner-notes moniker for every album (on Un Viaje, he's Sizu Yantra), his response to fans mistakenly calling him "Pinche Juan" ("Johnny Rotten") after a track of that name appeared on the band's debut disc. That's the sort of story he charmingly conveys during instrumental interludes.

"We try to involve the Anglo audience by presenting the ideas about the songs in English," Rangel says. "We want to make the people feel comfortable."

Stateside crowds have done their best to return the favor. Café Tacuba appeared at the Coachella music fest in California this year, after attending in the past as paying customers.

"We saw so many bands we admire," Rangel says. "And we got to play too, which is like an incredible bonus."

At Coachella and other U.S. tour stops, listeners who no hable Español have started crooning along with Albarrán's irresistible choruses, mimicking the strings of syllables even if they don't actually understand the words.

"What an incredible thing to hear," says Rangel, who maintains that it all sounds the same onstage, where nuances of pronunciation disappear in the din.

In some ways, Café Tacuba is an impressively uncompromising outfit. It's staunch about singing solely in Spanish, and it shifts styles significantly on each album. (On Cuatro Caminos, for example, it used live drums for the first time.) Yet it's also as accessible as experimental acts get, toning down sets if it feels the audience might be intimidated. It decorates its material with soccer-style chants, providing fans with an interactive arena-rock exercise that makes its manic genre-jumping feel less jarring.

"It's for the people, not only for the band," Rangel says. "Sometimes it's happened to me that I see a show and the band is playing for itself. This is a different approach. People can go there to feel happy."